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Observation of flat-band and band transition in the synthetic space

Constructions of synthetic lattices in photonics attract growingly attentions for exploring interesting physics beyond the geometric dimensionality, among which modulated ring resonator system has been proved as a powerful platform to create different kinds of connectivities between resonant modes along the synthetic frequency dimension with many theoretical proposals. Various experimental realizations are investigated in a single ring resonator, while building beyond simple synthetic lattices in multiple rings with different types remains lacking, which desires to be accomplished as an important step further. Here, we implement the experimental demonstration of generating the one-dimensional Lieb lattice along the frequency axis of light, realized in two coupled ring resonators while the larger ring undergoing dynamic modulation. Such synthetic photonic structure naturally exhibits the physics of flat band. We show that the time-resolved band structure read out from the drop-port output of the excited ring is the intensity projection of the band structure onto specific resonant mode in the synthetic momentum space, where gapless flat band, mode localization effect, and flat to non-flat band transition are observed in experiments and verified by simulations. Our work gives a direct evidence for the constructing synthetic Lieb lattice with two rings, which hence makes a solid step towards experimentally constructing more complicated lattices in multiple rings associated with synthetic frequency dimension.